Isospin symmetry and analyticity in D → K ¯ ππ $$ D\to \overline{K}\pi \pi $$ decays

Abstract We perform a detailed study of the consequences of isospin symmetry in the Cabibbo favoured D → K ¯ ππ $$ D\to \overline{K}\pi \pi $$ decays. These processes are important for precision testing of the Standard Model and for hadronic physics. Combining isospin symmetry with a dispersive reconstruction theorem we derive a representation in terms of one-variable functions which allows one to predict all the D → K ¯ ππ $$ D\to \overline{K}\pi \pi $$ amplitudes given inputs from one D + mode and one D 0 mode. From this, using dispersion relations and unitarity, we derive a set of 6+6 Khuri-Treiman type integral equations which enable to take three-body rescattering effects into account. A first test of this approach is presented using experimental results on the D + → K S π 0 π + and the D 0 → K S π − π + modes.